How to create reeling (spool) effect?
You can probably achieve better results with animation nodes similiar to cegaton's second linked answer. This answer will be the inaccurate, fast method. If you followed the linked tutorial, you can probably skip to step 4.


Use the Extra Objects Addon to add a curve spiral. Extrude the end of the spiral accordingly.

Add a subdivided plane. I created only a small stripe and used the array modifier. Use the curve modifier on the plane to deform it along the spiral curve.

Moving the plane will curl it around the spiral curve. Create two keyframes, making the curve roll around the spiral.

Add a spool cylinder. Currently the plane will initially not adhere to the spool, but rather curve around it with a gap between them. Select only the points which wrap around the curve and press &#9096; CtrlH  > Hook to new object. An empty will be created. I selected a cube as the empties shape.

Scaling the hook object will scale the hooked points. This way we can start with a smaller scale and shift the outer points of the spiral to the spool.

Go the end of the animation and keyframe the location of the plane and the scale of the hook empty. Go the the start of the animation, scale down the hook object and move the plane (along Y) and keyframes their respective values. You may have to add additional keyframes for the scale of the hook empty.